Question

The number of database queries made during any interval of time is a Poisson random variable....

The number of database queries made during any interval of time is a Poisson random variable. On average, six queries are made every minute. Determine the probability that three or more queries will be made during an interval of 15 seconds.

Homework Answers

Answer #1

Solution :

Given that ,

mean = = 6

Using poisson probability formula,

P(X = x) = (e- * x ) / x!

P(X 3) = 1 - P(X 2 )

= 1 - (  P(X = 0) + P(X = 1) + P(X = 2))

= 1 - (  (e6 * 60) / 0! + (e6 * 61) / 1! + (e6 * 62) / 2!

= 1 - (0.0025+0.0149+0.0446)

= 1 - 0.0620

= 0.9380

The probability that three or more queries will be made during an interval of 15 seconds is 0.9380.

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